The Impact of Multiscale Dataset and a Multi-Rate Gradient Descent Approach
Speaker: Liangchen Liu (UT Austin) Dates: 2024/10/24 Location: MW 154 Abstract: Data embedded in high-dimensional spaces often follows intrinsic low-dimensional structures, but assuming a consistent scale across all directions may be too idealized. Indeed, empirical observations suggest that data distributions tend…
Frenet immersed finite element methods for interface problems: Design, analysis and future directions
Speaker: Haroun Meghaichi (OSU) Dates: 2024/08/29 Location: MW 154 Abstract: In this talk, I will go over a brief survey of unfitted methods for interface problems with an emphasis on the immersed finite element method. Next, I will describe a…
Discrete fracture models for fluid flow in fracture porous media
Speaker: Ziyao Xu (UND) Dates: 2024/04/05 Location: zoom, link Abstract: As a result of geological processes and human activities, fractures are widely distributed in subsurface rocks. Depending on the degree of precipitation, fractures can act either as highly permeable, flow-preferential…
On the Activation Function Dependence of the Spectral Bias of Neural Networks
Speaker: Qinguo Hong (Missouri S&T) Dates: 2024/03/22 Location: MW 154 Abstract: Neural networks are universal function approximators which are known to generalize well despite being dramatically overparameterized. We study this phenomenon from the point of view of the spectral bias…
A High Order Geometry Conforming Immersed Finite Element for Elliptic Interface Problems
Speaker: Haroun Meghaichi (VT) Dates: 2024/02/08 Location: zoom Abstract:We present a high order immersed finite element (IFE) method for solving the elliptic interface problem with interface-independent meshes. The IFE functions developed here satisfy the interface conditions exactly and they have…
A Model-Based Approach for Continuous-Time Policy Evaluation with Unknown Lévy Process Dynamics
Speaker: Qihao Ye (UCSD) Dates: 2024/01/26 Location: zoom Abstract: This research presents a framework for evaluating policies in a continuous-time setting, where the dynamics are unknown and represented by Lévy processes. Initially, we estimate the model using available trajectory data,…
Exponentially Convergent Multiscale Methods Based on Edge Coupling: Example of Helmholtz Equation
Speaker: Yixuan Wang(Caltech) Dates: 2023/11/16 4-5pm Location: online, link Abstract:We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation….
BDDC Algorithms for Advection-diffusion problems with HDG Discretizations
Speaker: Jinjin Zhang (OSU) Dates: 2023/11/09 Location: MA 105 Abstract: In this talk, I will talk about the balancing domain decomposition by constraints (BDDC) methods for the non-symmetric positive definite system arising from the hybridizable discontinuous Galerkin (HDG) discretization of advection-diffusion…
Realizability-Preserving DG-IMEX Method for a Two-Moment Model of Special Relativistic Transport
Speaker: Joseph Hunter (OSU) Dates: 2023/11/01 Location: MA 105 Abstract: Special relativistic transport models are important for describing the transport of neutrinos, with applications to supernovae and gravitational waves. We study a two-moment model that evolves the Eulerian moments of…
Recent advances in discontinuous Galerkin discretization of Cahn–Hilliard–Navier–Stokes models for systems of two-phase flows
Speaker: Chen Liu (Purdue) Dates: 2023/10/26 Location: Zoom, link Abstract: Efficient and accurate pore-scale fluid dynamics simulators have important applications in digital rock physics. One of the popular approaches for modeling two-phase fluid flow in micro-to-millimeter pore structures is to…